The following hypothetical pulley system exists: A massless rope passes over a frictionless pulley. Particles of mass M and M+m are suspended from the two differents ends of the rope. If m=0, the tension T in the pulley rope is Mg. If instead the value m increases to infinity, the value of the tension will increase, approaching a finite constant.
Using F=ma, I understand that as m increases, the force will also increase. However, I don't understand why if m approaches infinity, then the tension will approach a constant value. Why is that? My understanding is that the F=ma equation would cause tension to approach infinity.
Additionally, if the conclusion in the hypothetical pulley system is correct, is it possible to find what constant the Tension would approach? If so, what would that value be, or how would it be calculated?